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Sunday, 5 January 2014

Numerical methods: ODE and Finite difference method

The goal of this post is show how solve an ordinary differential equation, numerically and using the finite difference method and compare the result with the analytic solution.
The problem statement is as follow:

Numerically solve the ODE: $m\frac{\partial^{2}y}{\partial t^{2}} = -b\frac{\partial y}{\partial t} $ that represents an object whose velocity at $t=0$ is equal to $v_0$ and it is slowing due to a retardant force, which is proportional to its velocity.